Simplify the following expression: $ k = \dfrac{3}{7} + \dfrac{a - 6}{-5} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5}{-5}$ $ \dfrac{3}{7} \times \dfrac{-5}{-5} = \dfrac{-15}{-35} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{a - 6}{-5} \times \dfrac{7}{7} = \dfrac{7a - 42}{-35} $ Therefore $ k = \dfrac{-15}{-35} + \dfrac{7a - 42}{-35} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{-15 + 7a - 42}{-35} $ $k = \dfrac{7a - 57}{-35}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{-7a + 57}{35}$